The present invention relates to use of scattered evanescent electromagnetic field for direct distance measurements. More specifically, the present invention relates to using evanescent electromagnetic field generated by total internal reflection for measuring separation between a sample and a probe in a scanning probe microscope.
One of the first techniques developed to measure surface forces of a sample was the development of the Surface Force Apparatus (SFA) in the 1970s which led to the first accurate measurement of many of such forces An SFA employs an interferometer using Fringes of Equal Chromatic Order (FECO). The distance between the silver-coated back-sides of mica sheets is determined from the wavelength of constructive interference for light in the gap between the silver layers. If one assumes that the thickness and refractive index of the mica sheets is constant throughout the measurement, then the thickness of a film intervening between the mica sheets can be measured using the wavelength at that thickness, and a three-layer optical model. The existence of a convenient wavelength standard (e.g. a mercury lamp) is a critical advantage for an interferometric technique such as FECO. The spectrometer wavelength can be frequently calibrated so that an absolute comparison can be made between wavelength measurement when the two mica sheets are in contact and the wavelength when there is an intervening film. In this sense, the SFA separation axis gives the absolute distance between mica sheets in some reference ‘contact’ position and all subsequent positions. Specifically, even after the adsorption of a thin film to the mica surface, the force can still be measured as a function of the separation between the mica sheets.
Scanning probe microscopes are the tools often used to profile a surface of a sample at an atomic level by approaching the surface with a probe and measuring tunneling currents or force between the tip of the probe and the surface. The tip of the probe may interact with the surface via a variety of surface effects, such as electron tunneling, interatomic forces, capacitive coupling, friction forces, magnetic forces, van der Waals forces, electrostatic double layer forces and other electrostatic forces, hydration forces, frictional forces, and oscillatory packing forces.
An Atomic Force Microscope (AFM), which is one of the types of the scanning probe microscopes, emerged in early 1990s as a as a valuable technique for surface force measurements, particularly when employed with a large spherical colloidal particle (r˜3 μm) attached to the force sensor. In an AFM, the probe is attached to a flexible cantilever or a spring, which in turn is attached to the force sensor. The probe can be a sharp tip (with the end radius of about 30 nm) or a spherical colloidal particle (with a radius of about 3 μm) which moves above the surface. If the cantilever control mechanism is constructed so that the force acting on the probe from the interaction with the surface remains constant, the probe will closely follow the profile of the surface. By detecting the motion of the cantilever (for example by detecting the reflection of a laser beam directed at it) it is therefore possible to determine the profile of the surface at the atomic level. These methods are known in the pertinent art and their details are beyond the scope of this invention.
Compared to the use of a sharp AFM tip, force measurement with a spherical colloidal particle (the colloid probe technique) improves the signal to noise ratio, and the known geometry allows the interpretation of results in terms of the energy per unit area, which is the intensive property used to compare forces in different geometries. The colloidal probe technique has many advantages including the ease of use of the instrument; the availability of AFMs in many research labs and the ability to measure forces on a variety of materials, including large colloidal particles and low probability of encountering contamination, as compared to the SFA technique. This latter advantage arises from the fact that the interacting area is about 104 times smaller in a Colloidal Probe measurement than in an SFA measurement.
It should be noted that there is no explicit measurement of the separation between the probe and the surface in an AFM colloidal probe measurement. The colloidal particle is attached to one end of a spring and the other end of the spring (the fixed end) is driven by a piezoelectric crystal (the piezo-drive) toward an interface while the deflection is monitored. Instead of a piezoelectric crystal, a different type of electromechanical transducer may be used as long as it is capable of transforming an electronic signal into a mechanical displacement. Zero force is established from the deflection of the spring far from contact where there is zero gradient in the curve of deflection versus piezo-drive displacement or distance, as shown by the force profiles in FIGS. 1A and 1B discussed below. Hereinafter, the piezo-drive distance means the distance between a probe and a sample inferred from the signal applied to the piezo-drive. Contact with the surface is inferred from the shape of the force curve. The contact between the colloidal probe and the other solid is assumed to occur when the slope of a curve of deflection versus piezo-drive distance is constant (the constant compliance regime). This assumption is based on the idea that surface forces are seldom changed linearly with distance, and that the interacting objects are rigid, so that they do not deform during the interaction. A linear spring is a spring producing a linear force, i.e., the force that is proportional to displacement, the coefficient of proportionality is called the spring constant. When all other components that connect the interacting surfaces are rigid, the load on the probe consists of only the linear AFM spring and the non-linear surface force. If the compound force is linear, either the surface force is zero, meaning that the particle is far away from the surface or the net surface force gradient is large (i.e., much larger than the spring constant of the cantilever), which would occur at contact. When the particle is far from the sample, the region of constant compliance is assumed to be where hard contact occurs between the solids.
In principle, the contact position in the AFM could be referenced to a standard position of the piezo-drive and a standard deflection of the cantilever. In practice, the contact position is measured on each force-separation curve. This leads to ambiguity when comparing force-separation runs under different conditions of the probe, surface, and the medium between them. The reason for establishing the zero on each force-separation run is that changes in the dimensions of equipment components due to fluctuations in the temperature (thermal drift) make it very inconvenient to produce a standard deflection of the cantilever or a standard position of the fixed end of the cantilever.
In AFM measurements, the constant compliance regime is also used to calibrate the deflection of the spring. The spring deflection is usually measured using the light-lever technique. A change in the end slope of the spring under an applied force produces a change in the angle of a laser beam reflected from the end of the cantilever. This change in angle causes a large displacement of the reflected beam if the displacement is measured far from the spring. The displacement of the reflected beam is calibrated by placing the colloidal probe in contact with a solid that is much stiffer than the cantilever spring. When the piezo-drive is used to reduce the separation between the fixed end of the spring and the solid sample, the deflection of the free end of the cantilever is equal to the distance moved by the piezo-drive if the solid is infinitely stiff. If the solid is known to be compliant, then the calibration must be performed independently on a stiff sample.
FIGS. 1A and 1B show an example of force measurement data obtained in a traditional colloid probe AFM experiment. These particular forces were measured between a borosilicate glass particle and a fused silica surface in an aqueous 0.9 mM (millimolar or millimole per liter) hexadecyltrimethylammonium bromide (CTABr) solution.
FIG. 1A shows non-calibrated dependence of deflection of a cantilever on distance of the probe from the surface. The deflection was measured using a spring-mounted lever. The deflection in region 1 (far from the surface) is defined to correspond to zero force. Region 2, where the slope is constant, is defined to be zero separation. This region is also used to calibrate the deflection of the cantilever. Note that in region 3, the slope is very nearly constant but the separation is not zero.
FIG. 1B shows calibrated deflection versus separation data obtained using FIG. 1A. The force is the deflection times a spring constant. The shape of the force curve in region 3 is obtained from the very small difference between the slopes in regions 2 and 3.
In summary, in FIGS. 1A and 1B the region of constant compliance is used both to determine the zero of distance and to calibrate the deflection of the cantilever. Problems arise when certain made assumptions are violated, the wrong region is chosen, or when the data collection error in this region is too large. An example of the wrong region is region 3 in FIGS. 1A and 1B, where the slope is almost constant, but a smaller separation was later achieved. The sudden discontinuities in FIG. 1A (at distance of about 60 nm and deflection of about 0) and FIG. 1B (at about 3.5 nm) make it clear that the solids are not touching in region 3. The data presented in FIGS. 1A and 1B illustrate that there is no unique method for uniquely identifying contact between the interfaces with a region of constant compliance. This is particularly problematic if the aim of the experiment is to determine the effect of an adsorbate on the surface force.
The Total Internal Reflection Microscopy (TIRM) technique was developed at about the same time as the colloidal probe technique to measure the relative energy of the particle at various separations. TIRM can be used to obtain the energy-separation profile of a colloidal particle that is unencumbered by a cantilever spring. The particle can rotate and translate, and over time will adopt a distribution of states with a frequency that is determined by the energy through the Boltzmann distribution. Thus, the TIRM technique measures the frequency-separation histogram, which is then used to determine the relative energy of the particle at various separations; there is no explicit measurement of force.
Total internal reflection is based on the following phenomenon. Electromagnetic radiation or an electromagnetic wave (for example, light) propagating in a medium, such as vacuum, a gas, a liquid, or a solid, may encounter a location where the medium interfaces another medium with different electromagnetic properties. Upon encountering this interface a portion of the incident radiation crosses the interface into the second medium and the remainder of the incident radiation propagates within the first medium in a different direction; this remainder is commonly called reflected radiation or reflected wave. Consider two uniform media separated by a plane with indices of refraction n1 and n2, respectively and imagine a line perpendicular or normal to the plane. When an electromagnetic wave approaches the planar interface from the first media at an angle θi to the line normal to the plane (called the angle of incidence), a portion of the wave enters the second media from the first at the angle θ2 to this normal line (called the angle of refraction). These angles are related by Snell's law (also called the refraction law): n1 sin θi=n2 sin θ2. As may be seen from this equation, when n1>n2, above a certain angle of incidence θi there is no angle of refraction θ2 that would fit the equation, because the value of sine is less or equal than one for any real angle θ2. At the angles above a certain angle of incidence (called critical angle) no portion of electromagnetic wave crosses the interface between the media, but the incident radiation is totally reflected back to the n1 medium, the phenomenon known as total internal reflection (TIR),
Direct measurement of a separation between the probe and the surface in a scanning probe microscope, such as an AFM, would have removed existing ambiguities from surface force measurements and would have allowed monitoring the forces at a known constant separation and exercising a much greater control over the position of the probe in the AFM applications.